Answer :
To determine which statement about the angle 199° is correct, we'll analyze it in terms of trigonometric properties based on its position in the unit circle.
1. Locating 199° on the Unit Circle:
- The angle 199° lies in the third quadrant because it is between 180° and 270°.
2. Trigonometric Functions in the Third Quadrant:
- In the third quadrant:
- The tangent function (tan) is positive.
- The cosine function (cos) is negative.
- The sine function (sin) is negative.
Let's now analyze each statement based on these properties:
A. tan 199° < 0
- Since the tangent of an angle in the third quadrant is positive, this statement is incorrect.
B. cos 199° < 0
- Since the cosine of an angle in the third quadrant is negative, this statement is correct.
C. sin 199° > 0
- Since the sine of an angle in the third quadrant is negative, this statement is incorrect.
Based on the analysis, the correct statement about 199° is:
B. cos 199° < 0
1. Locating 199° on the Unit Circle:
- The angle 199° lies in the third quadrant because it is between 180° and 270°.
2. Trigonometric Functions in the Third Quadrant:
- In the third quadrant:
- The tangent function (tan) is positive.
- The cosine function (cos) is negative.
- The sine function (sin) is negative.
Let's now analyze each statement based on these properties:
A. tan 199° < 0
- Since the tangent of an angle in the third quadrant is positive, this statement is incorrect.
B. cos 199° < 0
- Since the cosine of an angle in the third quadrant is negative, this statement is correct.
C. sin 199° > 0
- Since the sine of an angle in the third quadrant is negative, this statement is incorrect.
Based on the analysis, the correct statement about 199° is:
B. cos 199° < 0
